Question: Rewrite the expression in the form $z^n$. $\sqrt{\dfrac{z}{z^{^{\scriptsize\dfrac13}}}}=$
Explanation: $\begin{aligned} \sqrt{\dfrac{z}{z^{^{\scriptsize\dfrac13}}}}&=\sqrt{z^{^{ 1-\scriptsize\dfrac13}}} \\\\ &=\sqrt{z^{^{\scriptsize\dfrac23}}} \\\\ &=\left(z^{^{\scriptsize\dfrac23}}\right)^{^{\scriptsize\dfrac12}} \\\\ &=z{^{^{\scriptsize \dfrac23\cdot\dfrac12}}} \\\\ &=z{^{^{\scriptsize \dfrac13}}} \end{aligned}$